If y varies jointly as the product of x and z,and y=24;when x=3 and z=2.Find y when x=2 and z=5.
Well, well, well, let's unravel this joint venture, shall we? If y varies jointly as the product of x and z, we can write it as y = kxz, where k is our sweet little constant. Now, we're given that when x = 3 and z = 2, y = 24. So, using our equation, we have 24 = k * 3 * 2. Solving that equation will give us the value of k.
Once we have k, we can plug it in when x = 2 and z = 5 (keeping it in the family of course) to find our new y. So, let's do some pampering on this equation:
24 = k * 3 * 2
24 = 6k
k = 4
Now that we have k = 4, we can find our new y when x = 2 and z = 5:
y = k * x * z
y = 4 * 2 * 5
y = 40
So, when x = 2 and z = 5, y will be a swinging 40. Hope that brings a smile to your face!
To determine the value of y when x = 2 and z = 5, we can use the concept of joint variation.
1. Identify the given values and variables:
- y = 24 (given)
- x = 3 (given)
- z = 2 (given)
- x = 2 (to be determined)
- z = 5 (to be determined)
2. Set up the equation for joint variation:
y = k * x * z
3. Solve for the constant of variation, k, using the given values:
24 = k * 3 * 2
Divide both sides by (3 * 2) to isolate k:
k = 24 / 6
k = 4
4. Substitute the given values into the equation to solve for y when x = 2 and z = 5:
y = 4 * 2 * 5
y = 40
Therefore, when x = 2 and z = 5, y will be equal to 40.
To find y when x=2 and z=5, we need to determine the variation constant first.
The statement "y varies jointly as the product of x and z" can be written as a mathematical equation: y = kxz, where k is the variation constant.
To find the value of k, we can use the given values. In the first scenario, when x=3 and z=2, y=24. Plugging these values into the equation, we get:
24 = k * 3 * 2
Simplifying the equation, we divide both sides by 6:
4 = k
Now that we know k = 4, we can substitute this value into the equation with the new values for x=2 and z=5 to find y:
y = 4 * 2 * 5
y = 40
Therefore, when x=2 and z=5, y is equal to 40.
y = kxz, so y/xz is constant.
You want y such that
y/(2*5) = 24/(3*2)
y/10 = 24/6
now do your magic